SUMMARY: It is usually proposed to use a robotic manipulator for performing on-orbit capture of a target satellite in the planned active debris removal and on-orbit servicing missions. Control of the satellite-manipulator system is challenging because motion of the manipulator influences position and orientation of the chaser satellite. Moreover, the trajectory selected for the capture manoeuvre must be collision-free. In this article, we consider the case of a nonredundant manipulator mounted on a free-floating satellite.We propose to use the bi-directional rapidly-exploring random trees (RRT) algorithm to achieve two purposes: to plan a collision-free manipulator trajectory that, at the same time, will result in a desired change of the chaser satellite orientation. Several improvements are introduced in comparison to the previous applications of the RRT method for manipulator mounted on a free-floating satellite. Feasibility of the proposed approach is demonstrated in numerical simulations performed for the planar case in which the chaser satellite is equipped with a 2-DoF (Degree of Freedom) manipulator. The obtained results are analysed and compared with the results obtained from collision-free trajectory planning methods that do not allow to set the desired final orientation of the chaser satellite.